Geodesic
Topological transformations of three-dimensional dissipative solitons
Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 1, pp. 134-150
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We classify and analyze transformations of three-dimensional dissipative tangle-solitons, i.e., solitons with closed and nonclosed vortex lines, under smooth variations of the system parameters. An example of such a system is a laser medium with fast saturable absorption. We find several scenarios of both reversible and irreversible transformations and discuss the role of the dissipative property of the system (openness) in specific features of these phenomena.
Keywords: dissipative, laser, topological, three-dimensional soliton, hysteresis. 
@article{TMF_2020_203_1_a9,
     author = {N. N. Rosanov and S. V. Fedorov and N. A. Veretenov},
     title = {Topological transformations of three-dimensional dissipative solitons},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {134--150},
     year = {2020},
     volume = {203},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_203_1_a9/}
}
TY  - JOUR
AU  - N. N. Rosanov
AU  - S. V. Fedorov
AU  - N. A. Veretenov
TI  - Topological transformations of three-dimensional dissipative solitons
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2020
SP  - 134
EP  - 150
VL  - 203
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2020_203_1_a9/
LA  - ru
ID  - TMF_2020_203_1_a9
ER  - 
%0 Journal Article
%A N. N. Rosanov
%A S. V. Fedorov
%A N. A. Veretenov
%T Topological transformations of three-dimensional dissipative solitons
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2020
%P 134-150
%V 203
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2020_203_1_a9/
%G ru
%F TMF_2020_203_1_a9
N. N. Rosanov; S. V. Fedorov; N. A. Veretenov. Topological transformations of three-dimensional dissipative solitons. Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 1, pp. 134-150. http://geodesic.mathdoc.fr/item/TMF_2020_203_1_a9/

[1] L. D. Faddeev, Quantization of Solitons, Preprint IAS-75-QS70, Institute for Advanced Study, Princeton, 1975

[2] L. D. Faddeev, “Einstein and several contemporary tendencies in the field theory of elementary particle”, Relativity, Quanta and Cosmology, v. 1, eds. M. Pantaleo, F. de Finis, Johnson Repr. Corp., New York, 1979, 247–266 | MR

[3] L. D. Faddeev, A. J. Niemi, “Stable knot-like structures in classical field theory”, Nature, 387:6628, 58–61, arXiv: hep-th/9610193 | DOI

[4] L. D. Faddeev, A. J. Niemi, “Magnetic geometry and the confinement of electrically conducting plasmas”, Phys. Rev. Lett., 85:16 (2000), 3416–3419, arXiv: physics/0003083 | DOI

[5] E. Babaev, “Dual neutral variables and knot solitons in triplet superconductors”, Phys. Rev. Lett., 88:17 (2002), 177002, 4 pp., arXiv: cond-mat/0106360 | DOI

[6] J. Garaud, J. Carlström, E. Babaev, “Topological solitons in three-band superconductors with broken time reversal symmetry”, Phys. Rev. Lett., 107:19 (2011), 197001, 5 pp., arXiv: 1107.0995 | DOI

[7] D. Proment, M. Onorato, C. F. Barenghi, “Vortex knots in a Bose–Einstein condensate”, Phys. Rev. E, 85:3 (2012), 036306, 8 pp., arXiv: 1110.5757 | DOI

[8] D. Proment, M. Onorato, C. F. Barenghi, “Torus quantum vortex knots in the Gross–Pitaevskii model for Bose–Einstein condensates”, J. Phys.: Conf. Ser., 544:1 (2014), 012022, 10 pp. | DOI

[9] N. A. Veretenov, N. N. Rosanov, S. V. Fedorov, “Rotating and precessing dissipative-optical-topological-3D solitons”, Phys. Rev. Lett., 117:18 (2016), 183901, 5 pp. | DOI | MR

[10] N. A. Veretenov, S. V. Fedorov, N. N. Rosanov, “Topological vortex and knotted dissipative optical 3D solitons generated by 2D vortex solitons”, Phys. Rev. Lett., 119:26 (2017), 263901, 5 pp. | DOI

[11] S. V. Fedorov, N. A. Veretenov, N. N. Rosanov, “Irreversible hysteresis of internal structure of tangle dissipative optical solitons”, Phys. Rev. Lett., 122:2 (2019), 023903, 5 pp. | DOI

[12] N. A. Veretenov, S. V. Fedorov, N. N. Rosanov, “Topological three-dimensional dissipative optical solitons”, Proc. Roy. Soc. London Ser. A, 376:2124 (2018), 20170367, 11 pp. | DOI

[13] S. V. Fedorov, N. N. Rozanov, N. A. Veretenov, “Struktura energeticheskikh potokov v topologicheskikh trekhmernykh dissipativnykh solitonakh”, Pisma v ZhETF, 107:5 (2018), 342–346 | DOI | DOI

[14] N. N. Rozanov, M. V. Arkhipov, R. M. Arkhipov, N. A. Veretenov, A. V. Pakhomov, S. V. Fedorov, “Ekstremalnaya i topologicheskaya nelineinaya optika otkrytykh sistem”, Optika i spektroskopiya, 127:7 (2019), 82–93 | DOI | DOI

[15] N. N. Rosanov, S. V. Fedorov, N. A. Veretenov, “Laser solitons in 1D, 2D and 3D”, Eur. Phys. J. D, 73:7 (2019), 141, 15 pp. | DOI

[16] N. N. Rosanov, S. V. Fedorov, L. A, Nesterov, N. A. Veretenov, “Extreme and topological dissipative solitons with structured matter and structured light”, Nanomaterials, 9:6 (2019), 826 | DOI

[17] N. N. Rozanov, Dissipativnye opticheskie solitony. Ot mikro- k nano- i atto-, Fizmatlit, M., 2011

[18] N. N. Rozanov, “Kvaziopticheskoe uravnenie v sredakh so slabym pogloscheniem”, Optika i spektroskopiya, 127:9 (2019), 283–285 | DOI | DOI

[19] N. N. Rozanov, S. V. Fedorov, “Difraktsionnye volny pereklyucheniya i avtosolitony v lazere s nasyschayuschimsya poglotitelem”, Optika i spektroskopiya, 72:6 (1992), 1394–1399

[20] A. Kawauchi, A Survey of Knot Theory, Birkhäuser, Basel, 1996 | DOI | MR

[21] C. C. Adams, The Knot Book. An Elementary Introduction to the Mathematical Theory of Knots, W. H. Freeman, New York, 1994 | MR

[22] H. K. Moffatt, R. L. Ricca, “Helicity and the Călugăreanu invariant”, Proc. Roy. Soc. London Ser. A, 439:1906 (1992), 411–429 | DOI

[23] A. Villois, D. Proment, G. Krstulovic, “Universal and nonuniversal aspects of vortex reconnections in superfluids”, Phys. Rev. Fluids, 2:4 (2017), 044701, 17 pp., arXiv: 1612.00386 | DOI